A032303 "EFK" (unordered, size, unlabeled) transform of 2,1,1,1,...

1, 2, 1, 3, 3, 4, 6, 7, 9, 11, 15, 17, 22, 26, 32, 39, 47, 55, 67, 79, 93, 111, 130, 152, 178, 208, 241, 281, 325, 375, 433, 499, 571, 657, 751, 858, 980, 1116, 1268, 1442, 1635, 1851, 2095, 2367, 2669, 3011, 3389, 3809, 4281, 4803, 5383, 6030, 6746, 7538

Offset

0,2

Comments

Number of partitions of n into distinct parts with two kinds of one. - Andrew Howroyd, Jun 21 2018

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

C. G. Bower, Transforms (2)

Formula

G.f.: (1+2*x) * Product_{k=2..infinity} (1+x^k).

Prog

(PARI) {my(n=60); Vec((1+2*x)*prod(k=2, n, 1+x^k + O(x*x^n)))} \\ Andrew Howroyd, Jun 21 2018

Crossrefs

Cf. A032006.

Sequence in context: A366472 A130067 A282906 * A032215 A117363 A007307

Adjacent sequences: A032300 A032301 A032302 * A032304 A032305 A032306

Keyword

nonn

Author

Christian G. Bower

Extensions

a(0)=1 prepended and terms a(50) and beyond from Andrew Howroyd, Jun 21 2018

Status

approved